import functools
import gymnasium as gym
from math import log
import numpy as np
import tree  # pip install dm_tree
from typing import Optional

from ray.rllib.models.action_dist import ActionDistribution
from ray.rllib.models.torch.torch_modelv2 import TorchModelV2
from ray.rllib.utils.annotations import override, DeveloperAPI, ExperimentalAPI
from ray.rllib.utils.framework import try_import_torch
from ray.rllib.utils.numpy import SMALL_NUMBER, MIN_LOG_NN_OUTPUT, MAX_LOG_NN_OUTPUT
from ray.rllib.utils.spaces.space_utils import get_base_struct_from_space
from ray.rllib.utils.typing import TensorType, List, Union, Tuple, ModelConfigDict
from ray.rllib.utils.deprecation import deprecation_warning, Deprecated
from ray.util.debug import log_once

torch, nn = try_import_torch()


@DeveloperAPI
class TorchDistributionWrapper(ActionDistribution):
    """Wrapper class for torch.distributions."""

    @override(ActionDistribution)
    def __init__(self, inputs: List[TensorType], model: TorchModelV2):
        # If inputs are not a torch Tensor, make them one and make sure they
        # are on the correct device.
        if log_once("torch_distribution_wrapper_deprecation"):
            deprecation_warning(
                old=(
                    "ray.rllib.models.torch.torch_action_dist.Torch"
                    "DistributionWrapper"
                ),
                new="ray.rllib.models.torch.torch_distributions.",
            )
        if not isinstance(inputs, torch.Tensor):
            inputs = torch.from_numpy(inputs)
            if isinstance(model, TorchModelV2):
                inputs = inputs.to(next(model.parameters()).device)
        super().__init__(inputs, model)
        # Store the last sample here.
        self.last_sample = None

    @override(ActionDistribution)
    def logp(self, actions: TensorType) -> TensorType:
        return self.dist.log_prob(actions)

    @override(ActionDistribution)
    def entropy(self) -> TensorType:
        return self.dist.entropy()

    @override(ActionDistribution)
    def kl(self, other: ActionDistribution) -> TensorType:
        return torch.distributions.kl.kl_divergence(self.dist, other.dist)

    @override(ActionDistribution)
    def sample(self) -> TensorType:
        self.last_sample = self.dist.sample()
        return self.last_sample

    @override(ActionDistribution)
    def sampled_action_logp(self) -> TensorType:
        assert self.last_sample is not None
        return self.logp(self.last_sample)


@DeveloperAPI
class TorchCategorical(TorchDistributionWrapper):
    """Wrapper class for PyTorch Categorical distribution."""

    @override(ActionDistribution)
    def __init__(
        self,
        inputs: List[TensorType],
        model: TorchModelV2 = None,
        temperature: float = 1.0,
    ):
        if log_once("torch_distribution_wrapper_deprecation"):
            deprecation_warning(
                old=(
                    "ray.rllib.models.torch.torch_action_dist.Torch"
                    "DistributionWrapper"
                ),
                new=("ray.rllib.models.torch.torch_distributions." "TorchCategorical"),
            )
        if temperature != 1.0:
            assert temperature > 0.0, "Categorical `temperature` must be > 0.0!"
            inputs /= temperature
        super().__init__(inputs, model)
        self.dist = torch.distributions.categorical.Categorical(logits=self.inputs)

    @override(ActionDistribution)
    def deterministic_sample(self) -> TensorType:
        self.last_sample = self.dist.probs.argmax(dim=1)
        return self.last_sample

    @staticmethod
    @override(ActionDistribution)
    def required_model_output_shape(
        action_space: gym.Space, model_config: ModelConfigDict
    ) -> Union[int, np.ndarray]:
        return action_space.n


@DeveloperAPI
def get_torch_categorical_class_with_temperature(t: float):
    """TorchCategorical distribution class that has customized default temperature."""
    if log_once("torch_distribution_categorial_temp_deprecation"):
        deprecation_warning(
            old="ray.rllib.models.torch.torch_action_dist."
            "get_torch_categorical_class_with_temperature",
            new=("ray.rllib.models.torch.torch_distributions." "TorchCategorical"),
        )

    class TorchCategoricalWithTemperature(TorchCategorical):
        def __init__(self, inputs, model=None, temperature=t):
            super().__init__(inputs, model, temperature)

    return TorchCategoricalWithTemperature


@DeveloperAPI
class TorchMultiCategorical(TorchDistributionWrapper):
    """MultiCategorical distribution for MultiDiscrete action spaces."""

    @override(TorchDistributionWrapper)
    def __init__(
        self,
        inputs: List[TensorType],
        model: TorchModelV2,
        input_lens: Union[List[int], np.ndarray, Tuple[int, ...]],
        action_space=None,
    ):
        if log_once("torch_distribution_multi_categorical_deprecation"):
            deprecation_warning(
                old=(
                    "ray.rllib.models.torch.torch_action_dist." "TorchMultiCategorical"
                )
            )
        super().__init__(inputs, model)
        # If input_lens is np.ndarray or list, force-make it a tuple.
        inputs_split = self.inputs.split(tuple(input_lens), dim=1)
        self.cats = [
            torch.distributions.categorical.Categorical(logits=input_)
            for input_ in inputs_split
        ]
        # Used in case we are dealing with an Int Box.
        self.action_space = action_space

    @override(TorchDistributionWrapper)
    def sample(self) -> TensorType:
        arr = [cat.sample() for cat in self.cats]
        sample_ = torch.stack(arr, dim=1)
        if isinstance(self.action_space, gym.spaces.Box):
            sample_ = torch.reshape(sample_, [-1] + list(self.action_space.shape))
        self.last_sample = sample_
        return sample_

    @override(ActionDistribution)
    def deterministic_sample(self) -> TensorType:
        arr = [torch.argmax(cat.probs, -1) for cat in self.cats]
        sample_ = torch.stack(arr, dim=1)
        if isinstance(self.action_space, gym.spaces.Box):
            sample_ = torch.reshape(sample_, [-1] + list(self.action_space.shape))
        self.last_sample = sample_
        return sample_

    @override(TorchDistributionWrapper)
    def logp(self, actions: TensorType) -> TensorType:
        # # If tensor is provided, unstack it into list.
        if isinstance(actions, torch.Tensor):
            if isinstance(self.action_space, gym.spaces.Box):
                actions = torch.reshape(
                    actions, [-1, int(np.prod(self.action_space.shape))]
                )
            actions = torch.unbind(actions, dim=1)
        logps = torch.stack([cat.log_prob(act) for cat, act in zip(self.cats, actions)])
        return torch.sum(logps, dim=0)

    @override(ActionDistribution)
    def multi_entropy(self) -> TensorType:
        return torch.stack([cat.entropy() for cat in self.cats], dim=1)

    @override(TorchDistributionWrapper)
    def entropy(self) -> TensorType:
        return torch.sum(self.multi_entropy(), dim=1)

    @override(ActionDistribution)
    def multi_kl(self, other: ActionDistribution) -> TensorType:
        return torch.stack(
            [
                torch.distributions.kl.kl_divergence(cat, oth_cat)
                for cat, oth_cat in zip(self.cats, other.cats)
            ],
            dim=1,
        )

    @override(TorchDistributionWrapper)
    def kl(self, other: ActionDistribution) -> TensorType:
        return torch.sum(self.multi_kl(other), dim=1)

    @staticmethod
    @override(ActionDistribution)
    def required_model_output_shape(
        action_space: gym.Space, model_config: ModelConfigDict
    ) -> Union[int, np.ndarray]:
        # Int Box.
        if isinstance(action_space, gym.spaces.Box):
            assert action_space.dtype.name.startswith("int")
            low_ = np.min(action_space.low)
            high_ = np.max(action_space.high)
            assert np.all(action_space.low == low_)
            assert np.all(action_space.high == high_)
            return np.prod(action_space.shape, dtype=np.int32) * (high_ - low_ + 1)
        # MultiDiscrete space.
        else:
            # `nvec` is already integer. No need to cast.
            return np.sum(action_space.nvec)


@ExperimentalAPI
class TorchSlateMultiCategorical(TorchCategorical):
    """MultiCategorical distribution for MultiDiscrete action spaces.

    The action space must be uniform, meaning all nvec items have the same size, e.g.
    MultiDiscrete([10, 10, 10]), where 10 is the number of candidates to pick from
    and 3 is the slate size (pick 3 out of 10). When picking candidates, no candidate
    must be picked more than once.
    """

    def __init__(
        self,
        inputs: List[TensorType],
        model: TorchModelV2 = None,
        temperature: float = 1.0,
        action_space: Optional[gym.spaces.MultiDiscrete] = None,
        all_slates=None,
    ):
        if log_once("torch_distribution_multi_categorical_slate_deprecation"):
            deprecation_warning(
                old=(
                    "ray.rllib.models.torch.torch_action_dist."
                    "TorchSlateMultiCategorical"
                )
            )
        assert temperature > 0.0, "Categorical `temperature` must be > 0.0!"
        # Allow softmax formula w/ temperature != 1.0:
        # Divide inputs by temperature.
        super().__init__(inputs / temperature, model)
        self.action_space = action_space
        # Assert uniformness of the action space (all discrete buckets have the same
        # size).
        assert isinstance(self.action_space, gym.spaces.MultiDiscrete) and all(
            n == self.action_space.nvec[0] for n in self.action_space.nvec
        )
        self.all_slates = all_slates

    @override(ActionDistribution)
    def deterministic_sample(self) -> TensorType:
        # Get a sample from the underlying Categorical (batch of ints).
        sample = super().deterministic_sample()
        # Use the sampled ints to pick the actual slates.
        return torch.take_along_dim(self.all_slates, sample.long(), dim=-1)

    @override(ActionDistribution)
    def logp(self, x: TensorType) -> TensorType:
        # TODO: Implement.
        return torch.ones_like(self.inputs[:, 0])


@DeveloperAPI
class TorchDiagGaussian(TorchDistributionWrapper):
    """Wrapper class for PyTorch Normal distribution."""

    @override(ActionDistribution)
    def __init__(
        self,
        inputs: List[TensorType],
        model: TorchModelV2,
        *,
        action_space: Optional[gym.spaces.Space] = None
    ):
        if log_once("torch_action_dist_diag_gaussian_deprecation"):
            deprecation_warning(
                old="ray.rllib.models.torch.torch_action_dist.TorchDiagGaussian",
                new="ray.rllib.models.torch.torch_distributions.TorchDiagGaussian",
            )
        super().__init__(inputs, model)
        mean, log_std = torch.chunk(self.inputs, 2, dim=1)
        self.log_std = log_std
        self.dist = torch.distributions.normal.Normal(mean, torch.exp(log_std))
        # Remember to squeeze action samples in case action space is Box(shape)
        self.zero_action_dim = action_space and action_space.shape == ()

    @override(TorchDistributionWrapper)
    def sample(self) -> TensorType:
        sample = super().sample()
        if self.zero_action_dim:
            return torch.squeeze(sample, dim=-1)
        return sample

    @override(ActionDistribution)
    def deterministic_sample(self) -> TensorType:
        self.last_sample = self.dist.mean
        return self.last_sample

    @override(TorchDistributionWrapper)
    def logp(self, actions: TensorType) -> TensorType:
        return super().logp(actions).sum(-1)

    @override(TorchDistributionWrapper)
    def entropy(self) -> TensorType:
        return super().entropy().sum(-1)

    @override(TorchDistributionWrapper)
    def kl(self, other: ActionDistribution) -> TensorType:
        return super().kl(other).sum(-1)

    @staticmethod
    @override(ActionDistribution)
    def required_model_output_shape(
        action_space: gym.Space, model_config: ModelConfigDict
    ) -> Union[int, np.ndarray]:
        return np.prod(action_space.shape, dtype=np.int32) * 2


@DeveloperAPI
class TorchSquashedGaussian(TorchDistributionWrapper):
    """A tanh-squashed Gaussian distribution defined by: mean, std, low, high.

    The distribution will never return low or high exactly, but
    `low`+SMALL_NUMBER or `high`-SMALL_NUMBER respectively.
    """

    def __init__(
        self,
        inputs: List[TensorType],
        model: TorchModelV2,
        low: float = -1.0,
        high: float = 1.0,
    ):
        """Parameterizes the distribution via `inputs`.

        Args:
            low: The lowest possible sampling value
                (excluding this value).
            high: The highest possible sampling value
                (excluding this value).
        """
        if log_once("torch_action_dist_squashed_gaussian_deprecation"):
            deprecation_warning(
                old="ray.rllib.models.torch.torch_action_dist.TorchSquashedGaussian"
            )
        super().__init__(inputs, model)
        # Split inputs into mean and log(std).
        mean, log_std = torch.chunk(self.inputs, 2, dim=-1)
        # Clip `scale` values (coming from NN) to reasonable values.
        log_std = torch.clamp(log_std, MIN_LOG_NN_OUTPUT, MAX_LOG_NN_OUTPUT)
        std = torch.exp(log_std)
        self.dist = torch.distributions.normal.Normal(mean, std)
        assert np.all(np.less(low, high))
        self.low = low
        self.high = high
        self.mean = mean
        self.std = std

    @override(ActionDistribution)
    def deterministic_sample(self) -> TensorType:
        self.last_sample = self._squash(self.dist.mean)
        return self.last_sample

    @override(TorchDistributionWrapper)
    def sample(self) -> TensorType:
        # Use the reparameterization version of `dist.sample` to allow for
        # the results to be backprop'able e.g. in a loss term.

        normal_sample = self.dist.rsample()
        self.last_sample = self._squash(normal_sample)
        return self.last_sample

    @override(ActionDistribution)
    def logp(self, x: TensorType) -> TensorType:
        # Unsquash values (from [low,high] to ]-inf,inf[)
        unsquashed_values = self._unsquash(x)
        # Get log prob of unsquashed values from our Normal.
        log_prob_gaussian = self.dist.log_prob(unsquashed_values)
        # For safety reasons, clamp somehow, only then sum up.
        log_prob_gaussian = torch.clamp(log_prob_gaussian, -100, 100)
        log_prob_gaussian = torch.sum(log_prob_gaussian, dim=-1)
        # Get log-prob for squashed Gaussian.
        unsquashed_values_tanhd = torch.tanh(unsquashed_values)
        log_prob = log_prob_gaussian - torch.sum(
            torch.log(1 - unsquashed_values_tanhd**2 + SMALL_NUMBER), dim=-1
        )
        return log_prob

    def sample_logp(self):
        z = self.dist.rsample()
        actions = self._squash(z)
        return actions, torch.sum(
            self.dist.log_prob(z) - torch.log(1 - actions * actions + SMALL_NUMBER),
            dim=-1,
        )

    @override(TorchDistributionWrapper)
    def entropy(self) -> TensorType:
        raise ValueError("Entropy not defined for SquashedGaussian!")

    @override(TorchDistributionWrapper)
    def kl(self, other: ActionDistribution) -> TensorType:
        raise ValueError("KL not defined for SquashedGaussian!")

    def _squash(self, raw_values: TensorType) -> TensorType:
        # Returned values are within [low, high] (including `low` and `high`).
        squashed = ((torch.tanh(raw_values) + 1.0) / 2.0) * (
            self.high - self.low
        ) + self.low
        return torch.clamp(squashed, self.low, self.high)

    def _unsquash(self, values: TensorType) -> TensorType:
        normed_values = (values - self.low) / (self.high - self.low) * 2.0 - 1.0
        # Stabilize input to atanh.
        save_normed_values = torch.clamp(
            normed_values, -1.0 + SMALL_NUMBER, 1.0 - SMALL_NUMBER
        )
        unsquashed = torch.atanh(save_normed_values)
        return unsquashed

    @staticmethod
    @override(ActionDistribution)
    def required_model_output_shape(
        action_space: gym.Space, model_config: ModelConfigDict
    ) -> Union[int, np.ndarray]:
        return np.prod(action_space.shape, dtype=np.int32) * 2


@DeveloperAPI
class TorchBeta(TorchDistributionWrapper):
    """
    A Beta distribution is defined on the interval [0, 1] and parameterized by
    shape parameters alpha and beta (also called concentration parameters).

    PDF(x; alpha, beta) = x**(alpha - 1) (1 - x)**(beta - 1) / Z
        with Z = Gamma(alpha) Gamma(beta) / Gamma(alpha + beta)
        and Gamma(n) = (n - 1)!
    """

    def __init__(
        self,
        inputs: List[TensorType],
        model: TorchModelV2,
        low: float = 0.0,
        high: float = 1.0,
    ):
        if log_once("torch_action_dist_beta_deprecation"):
            deprecation_warning(
                old="ray.rllib.models.torch.torch_action_dist.TorchBeta"
            )
        super().__init__(inputs, model)
        # Stabilize input parameters (possibly coming from a linear layer).
        self.inputs = torch.clamp(self.inputs, log(SMALL_NUMBER), -log(SMALL_NUMBER))
        self.inputs = torch.log(torch.exp(self.inputs) + 1.0) + 1.0
        self.low = low
        self.high = high
        alpha, beta = torch.chunk(self.inputs, 2, dim=-1)
        # Note: concentration0==beta, concentration1=alpha (!)
        self.dist = torch.distributions.Beta(concentration1=alpha, concentration0=beta)

    @override(ActionDistribution)
    def deterministic_sample(self) -> TensorType:
        self.last_sample = self._squash(self.dist.mean)
        return self.last_sample

    @override(TorchDistributionWrapper)
    def sample(self) -> TensorType:
        # Use the reparameterization version of `dist.sample` to allow for
        # the results to be backprop'able e.g. in a loss term.
        normal_sample = self.dist.rsample()
        self.last_sample = self._squash(normal_sample)
        return self.last_sample

    @override(ActionDistribution)
    def logp(self, x: TensorType) -> TensorType:
        unsquashed_values = self._unsquash(x)
        return torch.sum(self.dist.log_prob(unsquashed_values), dim=-1)

    def _squash(self, raw_values: TensorType) -> TensorType:
        return raw_values * (self.high - self.low) + self.low

    def _unsquash(self, values: TensorType) -> TensorType:
        return (values - self.low) / (self.high - self.low)

    @staticmethod
    @override(ActionDistribution)
    def required_model_output_shape(
        action_space: gym.Space, model_config: ModelConfigDict
    ) -> Union[int, np.ndarray]:
        return np.prod(action_space.shape, dtype=np.int32) * 2


@Deprecated(
    old="ray.rllib.models.torch.torch_action_dist.TorchDeterministic",
    new="ray.rllib.models.torch.torch_distributions.TorchDeterminstic",
    error=False,
)
class TorchDeterministic(TorchDistributionWrapper):
    """Action distribution that returns the input values directly.

    This is similar to DiagGaussian with standard deviation zero (thus only
    requiring the "mean" values as NN output).
    """

    @override(ActionDistribution)
    def deterministic_sample(self) -> TensorType:
        return self.inputs

    @override(TorchDistributionWrapper)
    def sampled_action_logp(self) -> TensorType:
        return torch.zeros((self.inputs.size()[0],), dtype=torch.float32)

    @override(TorchDistributionWrapper)
    def sample(self) -> TensorType:
        return self.deterministic_sample()

    @staticmethod
    @override(ActionDistribution)
    def required_model_output_shape(
        action_space: gym.Space, model_config: ModelConfigDict
    ) -> Union[int, np.ndarray]:
        return np.prod(action_space.shape, dtype=np.int32)


@DeveloperAPI
class TorchMultiActionDistribution(TorchDistributionWrapper):
    """Action distribution that operates on multiple, possibly nested actions."""

    def __init__(self, inputs, model, *, child_distributions, input_lens, action_space):
        """Initializes a TorchMultiActionDistribution object.

        Args:
            inputs (torch.Tensor): A single tensor of shape [BATCH, size].
            model (TorchModelV2): The TorchModelV2 object used to produce
                inputs for this distribution.
            child_distributions (any[torch.Tensor]): Any struct
                that contains the child distribution classes to use to
                instantiate the child distributions from `inputs`. This could
                be an already flattened list or a struct according to
                `action_space`.
            input_lens (any[int]): A flat list or a nested struct of input
                split lengths used to split `inputs`.
            action_space (Union[gym.spaces.Dict,gym.spaces.Tuple]): The complex
                and possibly nested action space.
        """
        if log_once("torch_multi_action_dist_deprecation"):
            deprecation_warning(
                old=(
                    "ray.rllib.models.torch.torch_action_dist."
                    "TorchMultiActionDistribution"
                ),
                new="ray.rllib.models.torch.torch_distributions.TorchMultiDistribution",
            )
        if not isinstance(inputs, torch.Tensor):
            inputs = torch.from_numpy(inputs)
            if isinstance(model, TorchModelV2):
                inputs = inputs.to(next(model.parameters()).device)
        super().__init__(inputs, model)

        self.action_space_struct = get_base_struct_from_space(action_space)

        self.input_lens = tree.flatten(input_lens)
        flat_child_distributions = tree.flatten(child_distributions)
        split_inputs = torch.split(inputs, self.input_lens, dim=1)
        self.flat_child_distributions = tree.map_structure(
            lambda dist, input_: dist(input_, model),
            flat_child_distributions,
            list(split_inputs),
        )

    @override(ActionDistribution)
    def logp(self, x):
        if isinstance(x, np.ndarray):
            x = torch.Tensor(x)
        # Single tensor input (all merged).
        if isinstance(x, torch.Tensor):
            split_indices = []
            for dist in self.flat_child_distributions:
                if isinstance(dist, TorchCategorical):
                    split_indices.append(1)
                elif (
                    isinstance(dist, TorchMultiCategorical)
                    and dist.action_space is not None
                ):
                    split_indices.append(int(np.prod(dist.action_space.shape)))
                else:
                    sample = dist.sample()
                    # Cover Box(shape=()) case.
                    if len(sample.shape) == 1:
                        split_indices.append(1)
                    else:
                        split_indices.append(sample.size()[1])
            split_x = list(torch.split(x, split_indices, dim=1))
        # Structured or flattened (by single action component) input.
        else:
            split_x = tree.flatten(x)

        def map_(val, dist):
            # Remove extra categorical dimension.
            if isinstance(dist, TorchCategorical):
                val = (torch.squeeze(val, dim=-1) if len(val.shape) > 1 else val).int()
            return dist.logp(val)

        # Remove extra categorical dimension and take the logp of each
        # component.
        flat_logps = tree.map_structure(map_, split_x, self.flat_child_distributions)

        return functools.reduce(lambda a, b: a + b, flat_logps)

    @override(ActionDistribution)
    def kl(self, other):
        kl_list = [
            d.kl(o)
            for d, o in zip(
                self.flat_child_distributions, other.flat_child_distributions
            )
        ]
        return functools.reduce(lambda a, b: a + b, kl_list)

    @override(ActionDistribution)
    def entropy(self):
        entropy_list = [d.entropy() for d in self.flat_child_distributions]
        return functools.reduce(lambda a, b: a + b, entropy_list)

    @override(ActionDistribution)
    def sample(self):
        child_distributions = tree.unflatten_as(
            self.action_space_struct, self.flat_child_distributions
        )
        return tree.map_structure(lambda s: s.sample(), child_distributions)

    @override(ActionDistribution)
    def deterministic_sample(self):
        child_distributions = tree.unflatten_as(
            self.action_space_struct, self.flat_child_distributions
        )
        return tree.map_structure(
            lambda s: s.deterministic_sample(), child_distributions
        )

    @override(TorchDistributionWrapper)
    def sampled_action_logp(self):
        p = self.flat_child_distributions[0].sampled_action_logp()
        for c in self.flat_child_distributions[1:]:
            p += c.sampled_action_logp()
        return p

    @override(ActionDistribution)
    def required_model_output_shape(self, action_space, model_config):
        return np.sum(self.input_lens, dtype=np.int32)


@DeveloperAPI
class TorchDirichlet(TorchDistributionWrapper):
    """Dirichlet distribution for continuous actions that are between
    [0,1] and sum to 1.

    e.g. actions that represent resource allocation."""

    def __init__(self, inputs, model):
        """Input is a tensor of logits. The exponential of logits is used to
        parametrize the Dirichlet distribution as all parameters need to be
        positive. An arbitrary small epsilon is added to the concentration
        parameters to be zero due to numerical error.

        See issue #4440 for more details.
        """
        if log_once("torch_dirichlet_action_dist_deprecation"):
            deprecation_warning(
                old="ray.rllib.models.torch.torch_action_dist.TorchDirichlet",
            )
        self.epsilon = torch.tensor(1e-7).to(inputs.device)
        concentration = torch.exp(inputs) + self.epsilon
        self.dist = torch.distributions.dirichlet.Dirichlet(
            concentration=concentration,
            validate_args=True,
        )
        super().__init__(concentration, model)

    @override(ActionDistribution)
    def deterministic_sample(self) -> TensorType:
        self.last_sample = nn.functional.softmax(self.dist.concentration, dim=-1)
        return self.last_sample

    @override(ActionDistribution)
    def logp(self, x):
        # Support of Dirichlet are positive real numbers. x is already
        # an array of positive numbers, but we clip to avoid zeros due to
        # numerical errors.
        x = torch.max(x, self.epsilon)
        x = x / torch.sum(x, dim=-1, keepdim=True)
        return self.dist.log_prob(x)

    @override(ActionDistribution)
    def entropy(self):
        return self.dist.entropy()

    @staticmethod
    @override(ActionDistribution)
    def required_model_output_shape(action_space, model_config):
        return np.prod(action_space.shape, dtype=np.int32)
